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Research Papers: Design and Analysis

Stress Intensity Factors for Partially Autofrettaged Pressurized Thick-Walled Cylinders Containing Closely and Densely Packed Cracks

[+] Author and Article Information
Q. Ma

Edward F. Cross School of Engineering, Walla Walla University, College Place, WA 99324

C. Levy

Department of Mechanical and Materials Engineering, Florida International University, Miami, FL 33199

M. Perl

Department of Mechanical Engineering, Pearlstone Center for Aeronautical Engineering Studies, Ben Gurion University of the Negev, Beer Sheva 84105, Israel

J. Pressure Vessel Technol 132(5), 051203 (Aug 17, 2010) (9 pages) doi:10.1115/1.4001430 History: Received July 31, 2009; Revised March 08, 2010; Published August 17, 2010; Online August 17, 2010

Due to acute temperature gradients and repetitive high-pressure impulses, extremely dense internal surface cracks can be practically developed in highly pressurized thick-walled vessels, typically in gun barrels. In the authors’ previous studies, networks of typical radial and longitudinal-coplanar, semi-elliptical, internal surface cracks have been investigated assuming both ideal and realistic full autofrettage residual stress fields (ε=100%). The aim of the present work is to extend the analysis twofold: to include various levels of partially autofrettaged cylinders and to consider configurations of closely and densely packed radial crack arrays. To accurately assess the stress intensity factors (SIFs), significant computational efforts and strategies are necessary, especially for networks with closely and densely packed cracks. This study focuses on the determination of the distributions along the crack fronts of KIP, the stress intensity factor due to internal pressure KIA, the negative stress intensity factor resulting from the residual stress field due to ideal or realistic autofrettage, and KIN, the combined SIF KIN=KIP|KIA|. The analysis is performed for over 1000 configurations of closely and densely packed semicircular and semi-elliptical networked cracks affected by pressure and partial-to-full autofrettage levels of ε=30100%, which is of practical benefit in autofrettaged thick-walled pressure vessels. The 3-D analysis is performed via the finite element method and the submodeling technique employing singular elements along the crack front and the various symmetries of the problem. The network cracks will include up to 128 equally spaced cracks in the radial direction: with relative longitudinal crack spacing, 2c/d, from 0.1 to 0.99; autofrettage level of 30–100%; crack depth to wall thickness ratios, a/t, from 0.01 to 0.4; and, cracks with various ellipticities of crack depth to semicrack length, a/c, from 0.2 to 2. The results clearly indicate that the combined SIFs are considerably influenced by the three dimensionality of the problem and the Bauschinger effect (BE). The Bauschinger effect is found to have a dramatic effect on the prevailing combined stress intensity factors, resulting in a considerable reduction of the fatigue life of the pressure vessel. While the fatigue life can be finite for ideal autofrettage, it is normally finite for realistic autofrettage for the same crack network. Furthermore, it has been found that there are differences in the character of the SIFs between closely packed and densely packed crack networks, namely, more dramatic drop-offs in KIA and KIN at the crack-inner bore interface for densely packed cracks further influenced by crack depth.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Segment of crack network considered for the model employing planes of symmetry Z=0, θ=0, and θ=2π/n. The inset provides the definition of the angle ϕ for the SIF evaluation. (b) Cylinder segment employed in the FE model.

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Figure 2

The meshed submodel

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Figure 3

Normalized autofrettage SIF for closely packed, shallow, semicircular cracks a/c=1, a/t=0.05, 2c/d=0.25, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 4

Normalized autofrettage SIF for densely packed, shallow, semicircular cracks a/c=1, a/t=0.05, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 5

Normalized autofrettage SIF for closely packed, shallow, slender, semi-elliptical cracks a/c=0.5, a/t=0.05, and 2c/d=0.25, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols): (a) n=64 cracks in the radial direction and (b) n=128 cracks in the radial direction

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Figure 6

Normalized autofrettage SIF for densely packed, shallow, slender, semi-elliptical cracks a/c=0.5, a/t=0.05, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 7

Normalized autofrettage SIF for closely packed, shallow, transverse, semi-elliptical cracks a/c=1.5, a/t=0.05, 2c/d=0.25, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 8

Normalized autofrettage SIF for densely packed, shallow, transverse, semi-elliptical cracks a/c=1.5, a/t=0.05, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 9

Normalized autofrettage SIF for densely packed deeper, transverse, semi-elliptical cracks a/c=1.5, a/t=0.2, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 10

Normalized combined SIF for closely packed, shallow, semicircular cracks a/c=1, a/t=0.05, 2c/d=0.25, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 11

Normalized combined SIF for densely packed, shallow, semicircular cracks a/c=1, a/t=0.05, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 12

Normalized combined SIF for densely packed, semicircular cracks a/c=1, a/t=0.2, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 13

Normalized combined SIF for closely packed, shallow, slender, semi-elliptical cracks a/c=0.5, a/t=0.05, and 2c/d=0.25, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols): (a) n=64 cracks in the radial direction and (b) n=128 cracks in the radial direction

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Figure 14

Normalized combined SIF for densely packed, shallow, slender, semi-elliptical cracks a/c=0.5, a/t=0.05, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 15

Normalized combined SIF for densely packed, deeper, slender, semi-elliptical cracks a/c=0.5, a/t=0.2, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 16

Normalized combined SIF for closely packed, shallow, transverse, semi-elliptical cracks a/c=1.5, a/t=0.05, 2c/d=0.25, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 17

Normalized combined SIF for densely packed, shallow, transverse, semi-elliptical cracks a/c=1.5, a/t=0.05, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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Figure 18

Normalized combined SIF for densely packed, deeper, transverse, semi-elliptical cracks a/c=1.5, a/t=0.2, 2c/d=0.99, and n=64, for various autofrettage levels for BEIA (dark/solid symbols) and BEDA (clear/dashed symbols)

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